A comparison of moderate to extreme daily precipitation from the ERA-5 reanalysis by the European Centre for Medium-Range Weather Forecasts (ECMWF) against two observational gridded data sets, EOBS and CMORPH, is presented. We assess the co-occurrence of precipitation days and compare the full precipitation distributions. The co-occurrence is quantified by the hit rate. An extended generalized Pareto distribution is fitted to the positive precipitation distribution at every grid point and confidence intervals of quantiles compared. The Kullback-Leibler divergence is used to quantify the distance between the entire extended generalized Pareto distributions obtained from ERA-5 and the observations. For days exceeding the local 90th percentile, the mean hit rate is 65% between ERA-5 and EOBS (over Europe) and 60% between ERA-5 and CMORPH (globally). Generally, we find a decrease of the co-occurrence with increasing precipitation intensity. The agreement between ERA-5 and EOBS is weaker over the southern Mediterranean region and Iceland compared to the rest of Europe. Differences between ERA-5 and CMORPH are smallest over the oceans. Differences are largest over North-West America, Central Asia and land areas between 15°S and 15°N. The confidence intervals on quantiles are overlapping between ERA-5 and the observational data sets for more than 80% of the grid points on average. The intensity comparisons indicate an excellent agreement between ERA-5 and EOBS over Germany, Ireland, Sweden and Finland, and a disagreement over areas where EOBS uses sparse input stations. ERA-5 and CMORPH precipitation intensity agree well over the mid-latitudes and disagree over the tropics.